CS270 Midterm Fall 2014

I, the undersigned, do hereby affirm that the work contained in this exam is solely my own, and that none of the results were achieved by cheating. This includes using automated tools to generate answers, stealing the answers off the web, etc. Please do the work yourself. Name ____________________________________________________________________

(printed legibly) Signature____________________________________________________________________ 9-digit Student ID ____________________________________________________________

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Grading

Section

Possible Points

Actual Points

Number Representation 30

Floating Point Numbers 15

Combinational Logic 20

Sequential Logic 10

LC-3 Architecture 15

C Programming 10

Total 100

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Problems 1-10 are about number representation and number conversion, no calculators allowed! 1) How many bits in a byte and bytes in a 64-bit word? (2 points) ______________________, ______________________ 2) How many bits are required to represent 1015 unique patterns? How many are left over? (2 points) ______________________, ______________________ 3) What is the binary equivalent of the hexadecimal number 0xABCD0123? (2 points) 0b____________________________________________ 4) What is the hexadecimal equivalent of the binary number 0b1100010110011111? (2 points) 0x____________________________________________ 5) What is the decimal equivalent of the binary number 0b01110101? (2 points) ______________________________________________ 6) What is the binary equivalent of the decimal number 256 + 64 + 32 + 16 + 2 + 1 = 371? (2 points) 0b____________________________________________ 7) What is the (fixed-point) binary equivalent of the decimal number 5.625? (2 points) ____________________________________________

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8) What is the (fixed point) decimal equivalent of the binary number 1110.011? (2 points) _____________________________________________ 9) Translate the string “CS270” into decimal ASCII values (Hint: ASCII ‘A’ = 65, ASCII ‘0’ = 48). (3 points) ______ ______ ______ ______ ______ 10) What is the decimal value of the 8-bit 2’s complement binary number 0b11110110? (2 points) _________________________________ 11) Translate the decimal values below into 8-bit 2’s complement binary values and do the arithmetic. (6 points)

17 0b____________________ 32 0b____________________

+ 9 0b____________________ + -8 0b____________________

= 26 0b____________________ = 24 0b____________________

12) Show the result of the following logical operations in hexadecimal. Space is provided for binary values that may help you solve the problem but will not be graded (3 points)

0x76 0x76 0xFF & 0xBD | 0xBD ^ 0x0F = 0x = 0x = 0x

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Problems 13-15 should be answered based on the IEEE 754 single-precision format. HINT: 1 sign bit, 8 exponent bits, biased by 127, and 23 fractional bits, with an implicit 1. 13) What are the binary values of the fields of the IEEE 754 single-precision format of 12.25? (3 points) Sign = _____ Exponent: ___________________ Mantissa: 1.________________________________ 14) What is the decimal number represented by 0b 0 10000011 11000000000000000000000? (4 points) Show your work for partial credit: ________________________________________ 15) Fill in the values below for each step to add the floating point numbers x = 2.25 and y = 4.125. (8 points) x = 2.25 = 0x40100000, y = 4.125 = 0x40840000, sum = x + y What is the (unbiased) exponent of x, in decimal? ________________ What is the (unbiased) exponent of y, in decimal? ________________ What is the mantissa of x in binary, with the implicit 1 shown? 1.___________________________ What is the mantissa of y in binary, with the implicit 1 shown? 1.___________________________ What is the mantissa of the sum after normalization? 1.___________________________ What is the (unbiased) exponent of the sum, after normalization? _________________ What is the hexadecimal value of the sum? 0x_____________________________ What is the decimal value of the sum? _________________

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Problems 16-20 cover transistors, gates, and basic circuits. 16) Analyze the transistor circuits shown below and complete the truth table. Hint: A p-type transistor is closed

with 0 input and open with 1 input, an n-type transistor the opposite. (4 points)

A B T1 (p-type) T2 (p-type) T3 (n-type) T4 (n-type) C 0 0 Closed Open Open 0 1 Open 1 0 Closed 1 1 Open Closed Closed

17) How many select lines are needed for a 16 to 1 multiplexer? (2 points) __________________________________

18) For a 4-bit adder, what are the outputs for the inputs 0x8 and 0x9, if the CarryIn bit is 1. (4 Points) Sum = 0x_____________________, Carryout = ___________

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19) Analyze the combination logic shown below and complete the truth table. (6 Points)

A B X Y Z 0 0 0 1 1 0 1 1

20) Connect the output of the appropriate AND gates to the OR gates to fulfill the truth table below. (4 points)

A B X Y 0 0 1 0 0 1 0 0 1 0 0 1 1 1 1 1

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Problems 21 and 22 cover sequential logic and state machines. 21) Fill in the truth table for the D latch circuit show below. (5 points)

Data (D) Enable (EN) Previous State Output (Q) 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1

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22) If the state machine below starts in State 0 and is sent the input pattern 92, 44, 44, 11, 82, 29, 65, 12, what is the output and final state? (5 points)

Output: ___, ___, ___, ___, ___, ___, ___, ___ Final State: ________

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Problems 23-27 are related to LC-3 architecture and LC-3 assembly code. 23) What are the address space, word size, and number of registers on the LC-3 computer? (3 points) _________________, _________________, _________________ 24) Translate the following instruction into a hexadecimal value: AND R3,R6,#5 (3 points) 0x____________________________ 25) Translate the following hexadecimal value into an assembly instruction: 0x94FF (3 points) _____________________________________________ 26) What is in the PC offset field of the following LC-3 branch instruction? (3 points)

BRnp LABEL AND R2,R2,#0 AND R3,R3,#0

LABEL .FILL x1234 PC offset = __________________ 27) What are the values in R0, R1, and R2 after the following code executes? (3 points)

BR MAIN DATA0 .FILL xABCD DATA1 .FILL x1234 DATA2 .FILL xFFF6 MAIN LD R0, DATA0 LD R1, DATA1 LD R2, DATA2 BRp NEXT1 AND R0,R0,#0 NEXT1 NOT R0,R0 BRp NEXT2 AND R2,R2,xF NEXT2 ADD R1,R2,R1 HALT R0 = 0x_______________ R1 = 0x_______________ R2 = 0x_______________

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Questions 28-32 are related to the C program shown below, fill in what is printed. Note that the questions are in order of execution. (4 points each) #include <stdio.h> void doubleArray(int array[], int length) { for (int i = 0; i < length-2; i++) { array[i] += array[i]; } length += 5; printf(“%d\n”, length); // Question 29 } int main(int argc,char *argv[]) { int integers[6] = { 3, 4, 5, 6, 7, 8}; int length = 6; printf(“%d\n”, integers[4]); // Question 28 doubleArray(integers, length); printf(“%d\n”, *(integers + 3)); // Question 30 printf(“%d\n”, *(integers + 4)); // Question 31 printf(“%d\n”, length); // Question 32 } 28) ______________________________

29) ______________________________ 30) ______________________________

31) ______________________________ 32) ______________________________

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Appendix A) LC-3 Computer Schematic

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Appendix B) LC-3 Instruction Set

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Scratch paper, please do not put any answers here unless you reference this page in an answer!